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<h1 class="reftitle">LTISystem</h1>
<h2>Purpose</h2>
<p>Represents linear time-invariant systems</p>
<h2>Syntax</h2>
<pre class="synopsis">sys = LTISystem('A', A, 'B', B, 'C', C, 'D', D, 'T_s', Ts)</pre>
<h2>Description</h2>
<p></p> 
    This class represents linear time-invariant systems of the form
    <p class="programlistingindent"><img src="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem8.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem8.png"></p>
    where <img src="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem1.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem1.png"> is the state vector, <img src="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem2.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem2.png"> is the vector of inputs, <img src="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem3.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem3.png"> is the vector of outputs, and <img src="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem4.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem4.png">
    represents the sampling time.<br><br>

    Each LTI system defines following properties:
    <ul>
      
         <li>
            <tt>A</tt>, <tt>B</tt>: matrices of the
      state-update equation (read-only)</li>
      
         <li>
            <tt>C</tt>, <tt>D</tt>: matrices of the
      output equation (read-only)</li>
      
         <li>
            <tt>Ts</tt>: sampling time (read-only)</li>
      
         <li>
            <tt>nx</tt>, <tt>nu</tt>, <tt>ny</tt>: number of states,
      inputs and outputs (automatically determined, read-only)</li>
      
         <li>
            <tt>x</tt>: specifications of system's states (see <tt>help
      SystemSignal</tt>)</li>
      
         <li>
            <tt>u</tt>: specifications of system's inputs (see <tt>help
      SystemSignal</tt>)</li>
      
         <li>
            <tt>y</tt>: specifications of system's outputs (see <tt>help
      SystemSignal</tt>)</li>
    
      </ul>

    To define an LTI system, provide the list of system's matrices to
    the constructor:<br><br>
    
    
      <tt>sys = LTISystem('A', A, 'B', B, 'C', C, 'D', D, 'Ts', Ts)</tt>

    All inputs, except of the <tt>A</tt> matrix, can be omitted. In
    such a case they are set to empty matrices of corresponding
    dimension. As a consequence, one can easily define autonomous
    systems <img src="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem5.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem5.png"> by calling <tt> sys =
    LTISystem('A', A, 'f', f, 'Ts', Ts)</tt>. Similarly, to define an
    LTI system without outputs, call <tt>sys = LTISystem('A', A, 'B',
    B, 'Ts', Ts)</tt>. If the sampling time is omitted, it is set to
    <tt>Ts=1</tt>.<br><br>

    Another option to define an LTI system is to import the dynamics
    from Control toolbox' discre-time state-space objects:<br><br>

    
      <tt>sys = LTISystem(ss(A, B, C, D, Ts))</tt>

    Important to remember is that LTI systems carry with them the
    value of the state vector. The initial value can be set by the
    <tt>sys.initialize(x0)</tt> method (see "<tt>help
    LTISystem/initialize</tt>"). Value of the internal state can be
    retrieved by the <tt>sys.getStates()</tt> method (see "<tt>help
    LTISystem/getStates</tt>"). To update the internal state using the
    system's state-update equation, use the <tt>sys.update(u)</tt>
    function (see "<tt>help LTISystem/update</tt>").
  <h2>Example(s)</h2>
<h3>Example 
				1</h3>Create a 1D LTI system <img src="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem6.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem6.png">, <img src="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem7.png" alt="../../../../../fig/mpt/modules/ui/@LTISystem/ltisystem7.png">
      <pre class="programlisting">sys = LTISystem('A', 2, 'B', 1, 'C', 3)</pre>
<pre class="programlisting">LTISystem with 1 state, 1 input, 1 output
</pre>
<h2>See Also</h2>
<a href="../@PWASystem/pwasystem.html">pwasystem</a><p></p>
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<br><p>©  <b>2003-2013</b>     Michal Kvasnica: STU Bratislava,    <a href="mailto:michal.kvasnica@stuba.sk">michal.kvasnica@stuba.sk</a></p>
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